ALBANY — Even as New York rushes to spend hundreds of millions in federal stimulus money for roads and bridges, billions more for education, energy conservation and criminal justice remain untouched, according to federal officials.

A recent report from the US Government Accountability Office identified more than $3 billion awarded to New York but unspent at the end of June.

The state has spent about $700 million in stimulus funds so far on transportation projects and drawn about $2.6 billion in extra Medicaid money.

Yet it hadn’t spent a dime from some pots of money by the end of June.